Polynomial diffeomorphisms of C^2, IV: The measure of maximal entropy and laminar currents

This paper concerns the dynamics of polynomial automorphisms of ${\bf C}^2$. One can associate to such an automorphism two currents $\mu^\pm$ and the equilibrium measure $\mu=\mu^+\wedge\mu^-$. In this paper we study some geometric and dynamical properties of these objects. First, we characterize $\mu$ as the unique measure of maximal entropy. Then we show that the measure $\mu$ has a local product structure and that the currents $\mu^\pm$ have a laminar structure. This allows us to deduce information about periodic points and heteroclinic intersections. For example, we prove that the support of $\mu$ coincides with the closure of the set of saddle points. The methods used combine the pluripotential theory with the theory of non-uniformly hyperbolic dynamical systems

Classification of recurrent domains for some holomorphic maps

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46244/1/208_2005_Article_BF01446660.pd

Multi-messenger observations of a binary neutron star merger

On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of ~1.7 s with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of 40+8-8 Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 Mo. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at ~40 Mpc) less than 11 hours after the merger by the One- Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ~10 days. Following early non-detections, X-ray and radio emission were discovered at the transient’s position ~9 and ~16 days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta

Cardiovascular disease, chronic kidney disease, and diabetes mortality burden of cardiometabolic risk factors from 1980 to 2010: a comparative risk assessment.

Background: High blood pressure, blood glucose, serum cholesterol, and BMI are risk factors for cardiovascular diseases and some of these factors also increase the risk of chronic kidney disease and diabetes. We estimated mortality from cardiovascular diseases, chronic kidney disease, and diabetes that was attributable to these four cardiometabolic risk factors for all countries and regions from 1980 to 2010. Methods: We used data for exposure to risk factors by country, age group, and sex from pooled analyses of populationbased health surveys. We obtained relative risks for the eff ects of risk factors on cause-specific mortality from metaanalyses of large prospective studies. We calculated the population attributable fractions for- each risk factor alone, and for the combination of all risk factors, accounting for multicausality and for mediation of the eff ects of BMI by the other three risks. We calculated attributable deaths by multiplying the cause-specifi c population attributable fractions by the number of disease-specifi c deaths. We obtained cause-specifi c mortality from the Global Burden of Diseases, Injuries, and Risk Factors 2010 Study. We propagated the uncertainties of all the inputs to the fi nal estimates. Findings: In 2010, high blood pressure was the leading risk factor for deaths due to cardiovascular diseases, chronic kidney disease, and diabetes in every region, causing more than 40% of worldwide deaths from these diseases; high BMI and glucose were each responsible for about 15% of deaths, and high cholesterol for more than 10%. After accounting for multicausality, 63% (10\ub78 million deaths, 95% CI 10\ub71\u201311\ub75) of deaths from these diseases in 2010 were attributable to the combined eff ect of these four metabolic risk factors, compared with 67% (7\ub71 million deaths, 6\ub76\u20137\ub76) in 1980. The mortality burden of high BMI and glucose nearly doubled from 1980 to 2010. At the country level, age-standardised death rates from these diseases attributable to the combined eff ects of these four risk factors surpassed 925 deaths per 100 000 for men in Belarus, Kazakhstan, and Mongolia, but were less than 130 deaths per 100 000 for women and less than 200 for men in some high-income countries including Australia, Canada, France, Japan, the Netherlands, Singapore, South Korea, and Spain. Interpretation: The salient features of the cardiometabolic disease and risk factor epidemic at the beginning of the 21st century are high blood pressure and an increasing eff ect of obesity and diabetes. The mortality burden of cardiometabolic risk factors has shifted from high-income to low-income and middle-income countries. Lowering cardiometabolic risks through dietary, behavioural, and pharmacological interventions should be a part of the global response to non-communicable diseases